Campaigners including the writers Philip Pullman and Zadie Smith have lost their appeal to save six libraries from being closed by Brent council in London.

In what has been regarded as a test case, three judges at the court of appeal rejected claims by campaigners that the closure was "fundamentally flawed and unlawful", leading to fears that the "treasured" buildings could now be permanently closed.

The campaign group Brent SOS Libraries will now seek permission to appeal to the supreme court. "This is such an important issue – we don't believe the judge addressed the very real concerns that will be relevant to local authorities and library users and vulnerable groups up and down the country, so we will carry on," said the group's spokesperson Samantha Warrington.

She added that she hoped the court would agree to an appeal before Brent council moved to dispose of the libraries permanently. The group has already mounted vigils outside two of the libraries, Preston Road and Kensal Rise, to ensure that books and computers were not removed by the council.

The battle over Brent's libraries is viewed as a landmark case as councils implement cuts. In October, Pullman said the council's statement claiming that the closures would help "improve" its library services "ought to be quoted in every anthology of political bullshit from here to eternity."

The leader of Brent council, Councillor Ann John, said she was pleased with the appeal verdict. She added: "We will now be able to begin implementing the improvement plan that will deliver a better library service for the people of Brent." The council plans to replace the six libraries, one of which was opened by Mark Twain in 1900, with a £3m new library at Wembley. "The West End is closer to Brent residents than that," said campaigner Margaret Bailey.

The campaigners had claimed that Brent council had failed to take into account the impact the closures would have on vulnerable groups, including disabled and unemployed people as well as young children. However, Lord Justice Pill said: "Given the scale of the spending reductions the council was required to make and the information available following earlier studies, a decision that the library service should bear a share of the reduction was not, in my judgment, unlawful."

This is a matter of national importance," said Bailey. "Not just for libraries but for any kind of cuts to any kinds of services."

She added that the campaigners had sent Brent council a business plan for the community to run the library for no cost. "If they don't want to run the library, we're prepared to take on that task."